There have been recent interest on revisiting notion of observability in the context of networked control systems. In [1]}, the author revisit the notion of observability radius for a class of linear networks whose state matrices are adjacency matrix of some weighted graphs. They provide conditions to verify whether such networks can preserve observability property in presence of structured (weighted) edge perturbations. The authors also suggest a heuristic algorithm to compute size of perturbations that result in loss of observability by finding their
smallest Frobenius norm. In [2]} and [3]}, the problem of minimum constraint input selection are considered, where the objective is to find the smallest subset of inputs to ensure controllability. While it is shown that in general this problem is NP-hard, a subclass of such problems (by assuming dedicated inputs) can be solved efficiently with the aid of network graph algorithms. The author of [4]} shows that the problem of approximating the minimum number of input (output) variables to guarantee controllability (observability) is NP-hard. It is shown that one can find an efficient approximation of the problem by employing a greedy heuristic to select variables to maximize the rank increase of the controllability matrix. We refer to [5]} for some related background and earlier works in this context. In [6]}, the authors propose the problem of sensing-constrained LQG control, where contrary to the classical LQG, they look at the minimal sensing requirements for a desired control objective and tackle the problem by solving for suboptimal sensing strategies with by focusing only on finitely many sensing schedules.
They have also looked at batch sensor-scheduling for linear-time invariant control systems [7]}, where the goal is to design a sensing strategy to near-optimally estimate the concatenated states in a given finite horizon. In [8]}, classic Kalman filtering problems were extended to the case with intermittent observations.  Our work is close in spirit to [9]}, [10]}, where the authors investigate controllability of linear-time invariant networks and utilize randomized algorithms for sparsification [11]} and (greedy) deterministic algorithms to obtain a sparse actuator scheduling. Furthermore, by allowing scaling in control inputs, they show that one can achieve desired levels of performance with respect to a class of performance measures. Prior to their work, several authors had also considered problems related to sensor or actuator scheduling for control and estimation, for instance see [12]}, [13]}, [14]}, [15]} and the references therein. In another related work [16]}, the authors look at the sensor placement problem for optimal parameter estimation and provide a near-optimal greedy algorithm for sensor selection.
